In 1988, Worsey and Piper constructed a trivariate macro-element based on C1 quadratic splines defined over a split of a tetrahedron into 24 subtetrahedra. However, this local element can only be used to construct a corresponding macro-element spline space over tetrahedral partitions that satisfy some very restrictive geometric constraints. We show that by further refining their split, it is po...

This paper presents a parallel finite element toolbox for computing large electromagnetic devices on unstructured tetrahedral meshes, FEMAG—Fem for ElectroMagnetics on Adaptive Grids. The finite element toolbox deals with unstructured tetrahedral meshes and can solve electromagnetic eddy current problems in both frequency domain and time domain. It adopts high-order edge element methods and ref...

This paper uses simplicial complexes and simplicial (co)homology theory to expose a foundation for data structures for tetrahedral finite element meshes. Identifying tetrahedral meshes with simplicial complexes leads, by means of Whitney forms, to the connection between simplicial cochains and fields in the region modeled by the mesh. Furthermore, lumped field parameters are tied to matrices as...

Finite element simulation can be directly affected by mesh quality. The accuracy of finite element calculations is dependent upon of the mesh quality. Previously, we have introduced a novel approach to the construction of high-quality, isotropic tetrahedral meshes from segmented medical imaging data. This article proposes an experimental evaluation of the impact of our tetrahedral meshes on ele...

We propose a construction of a trivariate C 1 macro-element over a special tetrahedral partition and compare our construction with known C 1 macro-elements which are summarized in this paper. Also, we propose an improvement of the Alfeld construction of a C 1 quintic macro-element such that the new scheme is able to reproduce all polynomials of total degree 5. x1. Introduction The study of triv...

In this paper we present a new unstructured spectral element method for use on triangular and tetrahedral subdomains. The algorithm maintains the accuracy and efficiency of standard quadrilateral/hexahedral spectral element methods but offers greater adaptivity. Standard unstructured meshes can be used and the order of the polynomial expansion can be varied within each triangular/tetrahedral su...

This chapter explains techniques for the generation of quadrilateral and hexahedral element meshes. Since structured meshes are discussed in detail in other parts of this volume, we focus on the generation of unstructured meshes, with special attention paid to the 3D case. Quadrilateral or hexahedral element meshes are the meshes of choice for many applications, a fact that can be explained emp...

Tetrahedral meshes are often used for simulating deformable objects. Unlike engineering disciplines that often focuses on accuracy, computer graphics is biased towards stable, robust, and fast methods. In that spirit we present an approach for building an adaptive inward shell of the surface of an object. The goal is to device a simple and fast algorithm capable of building a topologically cons...